Solving Quadratic equations by factoring

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a quadratic equation?

Back

Factoring a quadratic equation involves rewriting it as a product of two binomials, such as (x - p)(x - q) = 0, where p and q are the roots of the equation.

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, set the equation to zero, factor the quadratic expression, and then set each factor equal to zero to find the solutions.

Front

What are the roots of the equation (x-5)(x+6)=0?

Back

The roots are x = 5 and x = -6.

Front

What is the first step in solving x² + 6x - 13 = 3?

Back

The first step is to make it equal to 0 by subtracting 3 from both sides, resulting in x² + 6x - 16 = 0.

Front

What is the factored form of 2x² + 7x + 6 = 0?

Back

The factored form is (2x + 3)(x + 2) = 0.

Front

What are the solutions to the equation 8n² + 10n - 3 = 0?

Back

The solutions are n = 1/4 and n = -3/2.

Front

What is the significance of the zero product property?

Back

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you find the roots of a quadratic equation?

Back

You can find the roots by factoring, using the quadratic formula, or completing the square.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.